电子束聚焦系统模型正椭圆周期解的存在性  

Existence of Positive Elliptic Periodic Solutions for the Electron Beam Focusing System Model

作　　者：章美月[1] 刘文斌[1] 张建军[1] 

机构地区：[1]中国矿业大学理学院,江苏徐州221116

出　　处：《中国矿业大学学报》2007年第6期864-868,共5页Journal of China University of Mining & Technology

基　　金：国家自然科学基金项目(10771212;10674177)

摘　　要：为了控制电子束的运动轨迹,使其有效地聚焦目标,对电子束聚焦系统数学模型的正椭圆周期解的存在性进行研究.利用Floquet理论得到了该方程的正椭圆周期解存在的条件;然后利用上下解方法和拓扑度的同伦不变性理论,证明了该模型正椭圆周期解的存在性定理,并进行了实例验证.结果表明:对该模型的系数取值范围的界定合理,正椭圆周期解的存在性定理正确,为进一步研究稳定性奠定了基础.In order to control the moving trace of electron beam and make it focus object effectually, the existence of positive elliptic periodic solution was studied based on the electron beam focusing system model. The condition for the existence of positive elliptic periodic solution was found using Floquet theory; and the theorem of the existence of positive elliptic periodic solution was proved by the method of upper and lower solutions and homotopy invariance theory of topology degree; then an example was given. The results show that the limited ranges of coefficient are reasonable and the theorem is right,which provide a basis for future study of stability.

关 键 词：电子束聚焦系统模型 椭圆周期解 FLOQUET理论 上下解 拓扑度 

分 类 号：O175.8[理学—数学]